Question: Simplify the following expression: $ q = \dfrac{3}{-4t - 3} - \dfrac{-9}{5} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{3}{-4t - 3} \times \dfrac{5}{5} = \dfrac{15}{-20t - 15} $ Multiply the second expression by $\dfrac{-4t - 3}{-4t - 3}$ $ \dfrac{-9}{5} \times \dfrac{-4t - 3}{-4t - 3} = \dfrac{36t + 27}{-20t - 15} $ Therefore $ q = \dfrac{15}{-20t - 15} - \dfrac{36t + 27}{-20t - 15} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{15 - (36t + 27) }{-20t - 15} $ Distribute the negative sign: $q = \dfrac{15 - 36t - 27}{-20t - 15}$ $q = \dfrac{-36t - 12}{-20t - 15}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{36t + 12}{20t + 15}$